A player at a basketball camp set a goal to make 55% if his shots. If he has 120 attempts, how many shots would he need to make in order to reach his goal?

a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

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Answer:

I guess the two angles have to be equal to 180°, so: 15x+48+5x+12=180

solve it:

20x+60=180

20x=180-60

20x=120

x=6 is the correct answer.

Answer:

Natural numbers are the counting numbers, meaning that they make up the set {1,2,3,4,5,...} So , 4/5 is belong to natural number

Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.

To find the maximum displacement, we need to first determine the particle's velocity and acceleration.

The velocity of the particle is given by the derivative of its position function:

\(v(t) = y'(t) = 3t^2 - 12t + 9\)

The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12

Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.

This occurs when its velocity is zero:

\(3t^2 - 12t + 9 = 0\)

Simplifying this equation, we get:

\(t^2 - 4t + 3 = 0\)

This quadratic equation factors as:

(t - 1)(t - 3) = 0

So the particle comes to rest at t = 1 or t = 3.

Next, we need to determine whether the particle is at a maximum or minimum at each of these times.

To do this, we look at the sign of the acceleration:

When t = 1, a(1) = 6(1) - 12 = -6, which is negative.

Therefore, the particle is at a maximum at t = 1.

When t = 3, a(3) = 6(3) - 12 = 6, which is positive.

Therefore, the particle is at a minimum at t = 3.

Finally, we need to find the displacement of the particle at each of these times:

\(y(1) = 1^3 - 6(1)^2 + 9(1) = 4\)

\(y(3) = 3^3 - 6(3)^2 + 9(3) = 0.\)

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Answer:

3. +4 get the number on the right. use division to isolate the variable. 7x. = 7. ® ... exs if x=9 y = 3 (9)²-66 y = 2/3 (81)-6 y = 54-6 y = 48 (again) if x=-6 or co, y = 18.

Step-by-step explanation:

A sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

To determine the sample size required to construct a 90% confidence interval for a population proportion with an error of 0.2 (or 20%), we need to use the formula for sample size calculation in proportion estimation.

The formula for sample size in proportion estimation is:

n = (Z² * p * q) / E²

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of approximately 1.645)

p = estimated or assumed population proportion (since there is no knowledge about the population proportion, we can assume a conservative value of 0.5 to get the maximum sample size)

q = 1 - p (complement of p)

E = desired margin of error (0.2 or 20% in this case)

Substituting the values into the formula:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.2²

n = (2.705 * 0.5 * 0.5) / 0.04

n = 0.67625 / 0.04

n ≈ 16.90625

Since the sample size must be a whole number, we round up the result to the nearest whole number:

n = 17

Therefore, a sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

It's important to note that this calculation assumes maximum variability in the population proportion (p = 0.5) to ensure a conservative estimate. If there is any information or prior knowledge available about the population proportion, it should be used to refine the sample size calculation.

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The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.

The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.

Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.

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The volume of the triangular prism on top is:

The volume of the rectangular prism underneath is:

Therefore, the total volume will be:

Two linear equations in two variables can be solved using the substitution techniques, graphical method or by the elimination method.

Let us consider any two real world linear equations in two variables.

x - y = 0

x + y = 4

Now let us first solve them by substitution method:

equation 1 can be written as : x = y ,

Now we substitute this value of x in the second equation:

x + y = 4

or,  y + y = 4

or, 2y = 4

or, y = 2

At x = 2 , y = 2. Hence the solution is (2,2)

Now let us solve by elimination method:

adding equation 1 and 2 we get:

x - y = 0

x + y = 4

2x = 4

or, x =2

at x=2 , y = 4-2 =2 Hence the solution is (2,2)

Now we will solve the equations graphical method.

In the graph attached below we can clearly see that the straight line representation of the two equations intersect at the point (2,2)

Hence the solution is (2,2) .

Therefore any linear equation in 2 variables can be solved by substitution , elimination and graphically.

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Answer:

-8

Step-by-step explanation:

It's basically -4-4. Which means -(4+4) = -8.

Answer:

b.

Step-by-step explanation:

b. i think so (:

Hello!

I am 99.9% sure the answer is D! The reason is literal equations use primarily of letters. An example of this would be  (A=πr2) or maybe  (v=Dt) to understand a little bit better.

~(˘▾˘~)

Answer:divideing by the whole number

Step-by-step explanation:

The factory overhead efficiency variance for May is $480 unfavorable.

What is overhead efficiency variance ?

The overhead efficiency variance measures the difference between the actual hours worked and the standard hours allowed, multiplied by the standard overhead rate.

Step 1: Budgeted overhead at 90% capacity:

Budgeted overhead = 6,120 DLHs * $3.00 per DLH = $18,360

Step 2: Budgeted overhead at 70% capacity:

Budgeted overhead = $15,640

Step 3: Standard hours at 70% capacity:

Standard hours = 6,120 DLHs / 90% * 70% = 4,760 DLHs

Step 4: Variable overhead rate:

Variable overhead rate = ($18,360 - $15,640) / (6,120 DLHs - 4,760 DLHs) = $2.00 per DLH

Step 5: Variable overhead efficiency variance:

Variable overhead efficiency variance = (4,760 DLHs - 5,000 DLHs) * $2.00 = $480 unfavorable

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Answer:

727

Step-by-step explanation:

6^3-106^2=216+360=576+168=744-17=727

The equation of the ellipse having a major axis of length 10 and foci at (1, 5) and (1, 1) is (x - 1)²/100 + (y - 3)²/16 = 1. So, the correct answer is option B.

The equation of an ellipse is given by (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center of the ellipse and a and b are the length of the major and minor axes respectively.

Since the major axis of the given ellipse has a length of 10, we can set a = 10. The two foci of the ellipse are given as (1, 5) and (1, 1) which means the center of the ellipse is the midpoint of these two foci, i.e., (1, 3). Therefore, h = 1 and k = 3.

We also need to calculate the length of the minor axis, b. We can calculate this value using the distance formula,

d = √((x2 - x1)² + (y2 - y1)²)

Therefore,

b = √((12 - 12)² + (52 - 12)²)

 = √(0 + 16)

 = 4

Therefore, the equation of the ellipse with a major axis on length 10 contains foci at (1, 5) and (1, 1) is given by (x - 1)²/100 + (y - 3)²/16 = 1.

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Complete Question:

Find  an equation of the ellipse having a major axis of length 10 with foci at (1, 5) and (1, 1):

A. (x - 1)²/100 + (y - 3)²/4 = 1

B. (x - 1)²/100 + (y - 3)²/16 = 1

C. (x - 1)²/25 + (y - 3)²/4 = 1

D. (x - 1)²/25 + (y - 3)²/16 = 1

The change that increases the loudness is a > 1

From the question, the equation of the function that represents the musical note is given as

y = a sin(1320πx)

Where

In sound, the sound loudness is directly proportional to the amplitude.

This means that an increment in the amplitude, would cause the note to become louder

This change is represented as a > 1

This is so because a represents the amplitude, and the initial value is 1

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If a (30cm by 40cm) page of a book includes a 2cm margin on each side, then the margins occupy 11.67 percentage of the total surface area of one side of the pages.

As per the question statement, a (30cm by 40cm) page of a book includes a 2cm margin on each side.

We are required to calculate the percentage of the total surface area of one side of the pages, occupied by the margins.

To solve this question, first we will need to calculate the total surface area of one side of the pages, and also the surface area occupied by the margins on one side, and then simply, calculate the percentage amount between the two area values.

Since the dimensions of the pages of the book are (30cm by 40cm), therefore, area of one side of each page = (30 * 40) sq. cm.

                                                                    = 1200 sq. cm.

And, area occupied by the margins on each side of the page

= [(2 * 30) + (2 * 40)] sq. cm.

= (60 + 80) sq. cm.

= 140 sq. cm.

Therefore, percentage of the total surface area of one side of the pages, occupied by the margins = [(140/1200) * 100] = 11.67%

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ANSWER

EXPLANATION

We want to simplify the expression given:

To do this, we have:

Multiply two of the expressions in brackets and then simplify by multiplying the result with the last expression:

That is the answer.

Answer:

the answer is 24/25

hope it helps have a nice day! :)

Answer:

8 cm and 9 cm

Step-by-step explanation:

got it right!

Answer:

8cm 9cm

Step-by-step explanation:

Given the cone z² = x²y² and the point (5, 3, 0), we have to find the points on the cone that are closest to the given point.The equation of the cone z² = x²y² can be written in the form z² = k²(x² + y²), where k is a constant.

Hence, the cone is symmetric about the z-axis. Let's try to obtain the constant k.z² = x²y² ⇒ z = ±k√(x² + y²)The distance between the point (x, y, z) on the cone and the point (5, 3, 0) is given byD² = (x - 5)² + (y - 3)² + z²Since the points on the cone have to be closest to the point (5, 3, 0), we need to minimize the distance D. Therefore, we need to find the values of x, y, and z on the cone that minimize D².

Let's substitute the expression for z in terms of x and y into the expression for D².D² = (x - 5)² + (y - 3)² + [k²(x² + y²)]The values of x and y that minimize D² are the solutions of the system of equations obtained by setting the partial derivatives of D² with respect to x and y equal to zero.∂D²/∂x = 2(x - 5) + 2k²x = 0 ⇒ (1 + k²)x = 5∂D²/∂y = 2(y - 3) + 2k²y = 0 ⇒ (1 + k²)y = 3Dividing these equations gives us x/y = 5/3. Substituting this ratio into the equation (1 + k²)x = 5 gives usk² = 16/9 ⇒ k = ±4/3Now that we know the constant k, we can find the corresponding value of z.z = ±k√(x² + y²) = ±(4/3)√(x² + y²)

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9 + x

sum = addition so the answer would be 9 + ×

Answer:

a b c and e

Step-by-step explanation:

hope it helped :3

=======================================================

Explanation:

Let's go through the answer choices to see which are true or which are false.

To help us out, we'll use the graph which I've posted below (attached image).

We can estimate with 98% confidence that the true proportion of women in Europe who use the internet lies within the range of 0.513 to 0.603.

Based on the given study of 600 internet users in Europe, where 335 of them were women, we can estimate the true proportion of women in Europe who use the internet using a confidence interval.

To calculate the confidence interval for the true proportion of women, we can use the formula:

CI = \($\hat{p}$\) ± z * √(\($\hat{p}$\)(1-\($\hat{p}$\)) / n)

where:

\($\hat{p}$\) is the sample proportion of women (335/600)

z is the z-score corresponding to the desired level of confidence (98% corresponds to a z-score of approximately 2.33)

n is the sample size (600)

Plugging in the values, we can calculate the confidence interval:

\($\hat{p}$\) = 335/600 = 0.5583

z = 2.33

n = 600

CI = 0.5583 ± 2.33 * √((0.5583 * (1-0.5583)) / 600)

Calculating the expression inside the square root, we get:

√((0.5583 * (1-0.5583)) / 600) ≈ 0.0221

Therefore, the confidence interval estimate for the true proportion of women in Europe who use the internet is:

CI = 0.5583 ± 2.33 * 0.0221

This can be further simplified as:

CI = (0.513, 0.603)

Thus, we can estimate with 98% confidence that the true proportion of women in Europe who use the internet lies within the range of 0.513 to 0.603.

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The lowest common denominator is 120.

Convert 3/4: 90/120

Convert 4/5: 96/120

Convert 5/6: 100/120

Firm 1 and Firm 2 will produce the same quantity and charge the same price in this scenario.

To determine the price, quantity, and profit for Firm 1 and Firm 2, we need to analyze the market equilibrium. In a competitive market, the price and quantity are determined by the intersection of the market demand and the total supply.

Market Demand:

The market demand is given by the equation P = 100 - Q, where P represents the price and Q represents the total quantity demanded in the market.

Total Cost:

Both firms have identical total cost functions, which are not explicitly provided in the question. However, we can assume that the total cost function for each firm is given by TC = C + MC * Q, where TC represents the total cost, C represents the fixed cost, MC represents the marginal cost, and Q represents the quantity produced by the firm.

Given that the marginal cost is MC = 4 + Q, we can rewrite the total cost function as TC = C + (4 + Q) * Q.

Market Equilibrium:

To find the market equilibrium, we set the market demand equal to the total supply. In this case, since Firm 1 can charge any price that Firm 2 charges, both firms will produce the same quantity and charge the same price.

Market Demand: P = 100 - Q

Total Supply: QS = Q1 + Q2 (quantity produced by Firm 1 and Firm 2)

Setting the market demand equal to the total supply, we have:

100 - Q = Q1 + Q2

Since Firm 1 and Firm 2 have identical total cost functions, they will split the market equilibrium quantity equally. Therefore, Q1 = Q2 = Q/2.

Substituting Q1 = Q2 = Q/2 into the equation 100 - Q = Q1 + Q2, we get:

100 - Q = Q/2 + Q/2

100 - Q = Q

Solving this equation, we find Q = 50. Thus, both Firm 1 and Firm 2 will produce 50 units of output.

Price Calculation:

To calculate the price, we substitute the quantity (Q = 50) into the market demand equation:

P = 100 - Q

P = 100 - 50

P = 50

Therefore, both Firm 1 and Firm 2 will charge a price of 50.

Profit Calculation:

To calculate the profit for each firm, we subtract the total cost from the total revenue. The total revenue for each firm is given by the product of the price (P = 50) and the quantity (Q = 50).

Total Revenue (TR) = P * Q = 50 * 50 = 2500

The total cost function for each firm is TC = C + (4 + Q) * Q. Since the fixed cost (C) is not provided, we cannot determine the profit explicitly. However, we can compare the profit of Firm 1 and Firm 2 if their total costs are the same.

Since both firms have identical total cost functions, they will have the same profit when their costs are the same. If their costs differ, then the firm with lower costs will have higher profits.

Overall, both Firm 1 and Firm 2 will produce 50 units of output, charge a price of 50, and their profits will depend on their total costs, which are not explicitly provided in the question.

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Division is one of the four fundamental arithmetic operations. The number of machines that will be needed to produce 1,984 printers in a day is 32 machines.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that 20 machines produce 1,240 printers in a day. Therefore, the rate of production for a single machine can be written as,

Rate of production for a day = 1240/20 = 62 printer per machine

Now, the number of machines that will be needed to produce 1,984 printers in a day is,

Rate of production for a day = 1,984 / Number of machine

62 = 1984 / Number of machine

Number of machines = 32 machines

Hence, the number of machines that will be needed to produce 1,984 printers in a day is 32 machines.

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Answer:

try C=5B

Step-by-step explanation:

The inequality w > 4 can be used to complete the following statements: The w in the inequality is the variable or unknown value being compared with the number 4. It represents an unknown quantity that is greater than 4.

The 4 in the inequality is the constant or known value that the variable w is being compared to. It is a number that is less than w.  

Inequalities use mathematical symbols to compare two values and express their relationship.

In this case, the inequality w > 4 uses the symbol ">" which means "greater than." The inequality indicates that w is larger than 4, so any value of w that is greater than 4 will make the inequality true.

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